Coronal expansion and solar wind

1
Coronal expansion and solar wind

• The large solar corona
• Coronal and interplanetary temperatures
• Coronal expansion and solar wind
• The heliosphere
• Origin of solar wind in magnetic network
• Multi-fluid models of the solar wind

2
The visible solar corona
Eclipse 11.8.1999
3
Electron density in the corona

• Current sheet and streamer belt, closed
• Polar coronal hole, open magnetically

Heliocentric distance / Rs
Guhathakurta and Sittler, 1999, Ap.J., 523, 812
Skylab coronagraph/Ulysses in-situ
4
Electron temperature in the corona
Streamer belt, closed Coronal hole, open
magnetically
David et al., AA, 336, L90, 1998
SUMER/CDS SOHO
Heliocentric distance
5
Coronal magnetic field and density
Dipolar, quadrupolar, current sheet contributions
Polar field B 12 G
Current sheet is a symmetric disc anchored at
high latitudes !
Banaszkiewicz et al., 1998 Schwenn et al., 1997
LASCO C1/C2 images (SOHO)
6
Solar wind stream structure and heliospheric
current sheet
Parker, 1963
Alfven, 1977
7
Solar wind fast and slow streams
Helios 1976
Marsch, 1991
Alfvén waves and small-scale structures
8
Model of coronal-heliospheric field
Fisk
Parker
Fisk, JGR, 1996
9
Heliospheric temperatures
Halo (4) Core (96)
Electrons
Tp ? Te
Protons
McComas et al., 1998
Ulysses
10
Correlations between wind speed and corona
temperature
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Fast solar wind parameters

• Energy flux at 1 RS FE 5 105 erg cm-2
  s-1
• Speed beyond 10 RS Vp (700 - 800) km
  s-1
• Proton flux at 1 AU np Vp 2 108 cm-2 s-1
• Density at 1 AU np 3 cm-3 n?/np
  0.04
• Temperatures at 1 AU
• Tp 3 105 K T? 106 K Te 1.5
  105 K
• Heavy ions Ti ? mi / mp Tp Vi -
  Vp VA

Schwenn and Marsch, 1990, 1991
12
On the source regions of the fast solar wind in
coronal holes
Insert SUMER Ne VIII 770 Å at 630 000
K Chromospheric network Doppler shifts Red
down Blue up Outflow at lanes and junctions
Image EIT Corona in Fe XII 195 Å at 1.5 M K
Hassler et al., Science 283, 811-813, 1999
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The source regions of the fast solar wind in
polar coronal holes
SUMER Ne VIII 770 Å at 630 000 K Encircled
contours Doppler shift gt 5 km/s Radiance Sept
ember 21, 1996
Doppler-shift map of solar polar cap 520" ?
300" gliding step size 3"
Wilhelm et al., AA, 353, 749, 2000
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Magnetic network loops and funnels
Structure of transition region Magnetic
field of coronal funnel

FB AB FM A?V
A(z) flux tube cross section
Dowdy et al., Solar Phys., 105, 35, 1986
Hackenberg et al., Space Sci. Rev., 87, 207, 1999
15
Height profiles in funnel flows
T / K
V / km s-1
1000
106
100
105
10
1 10 100 1000 1
10 100 1000
Height / M m
Height / M m

• Critical point at 1 RS

• Heating by wave sweeping
• Steep temperature gradients

Hackenberg, Marsch, Mann, AA, 360, 1139, 2000
16

Heating and acceleration of ions by cyclotron and
Landau resonance
Doppler broadening Thermal speed
Temperature
T(2-6) MK r 1.15 RS
? ? Z/A
Tu et al., Space Sci. Rev., 87, 331, 1999
Ion heating ? mass/charge
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Outflow speed in interplume region at the coronal
base
1.05 RS EIT FeIX/X Eclipse 26/02 1998
1833 UT
SUMER
67 km/s
O VI 1031.9 Å / 1037.2 Å line ratio Doppler
dimming
Patsourakos and Vial, AA, 359, L1, 2000
Te Ti 0.9 M K, ne 1.8 107 cm-3
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Oxygen and hydrogen thermal speeds in coronal
holes
Very Strong perpendicular heating of Oxygen !
Cranmer et al., Ap. J., 511, 481, 1998
Large anisotropy TO?/TO?? ? 10
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Fast solar wind speed profile
IPS
Ulysses
V (km s-1)
Lyman Doppler dimming
mass flux continuity
Radial distance / Rs
Esser et al., ApJ, 1997
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Boundaries of coronal holes
White lines CH boundaries in He 10830 Å
Ulysses data based MHD model
Mikic Linker, 1998
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Solar wind in Carrington longitude
Bins 50 x 50 Rotations 1891-1895
Neugebauer, et al., JGR 103, 14587, 1998
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Polar diagram of solar wind
SWICS Ulysses
Ecliptic
Near solar maximum Slow wind at - 65 !
Woch, 2000
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Heliosphere and local interstellar medium
V 25 km/s
Bow shock
Heliopause
Hydrogen wall
Heliospheric SW shock
(red) - 0.3 gt log(ne/cm3) gt - 3.7 (blue)
Kausch, 1998
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Solar wind speed and density
Polar diagram V
B outward
Density n R2
Ecliptic
B inward
McComas et al., GRL, 25, 1, 1998
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Rotation of solar corona
Fe XIV 5303 Å Time series 1 image/day (24-hour
averages)
27.2 days
Rotation periods of coronal features
LASCO/SOHO
Long-lived coronal patterns exhibit uniform
rotation at the equatorial rotation period!
Stenborg et al., 1999
26
Suns loss of angular momentum carried by the
solar wind I
Induction equation ? x (V x B) 0 --gt
r (VrB? - BrV?) - r0B0?0r0
Momentum equation ?V?? V? 1/4? B??B?
--gt r (? VrV? - BrB?) 0 L ?0rA2
(specific angular momentum)
V? ?0r (MA2 (rA/r)2 -1)/(MA2 -1)
MA Vr(4??)1/2/Br
Alfvén Machnumber
Helios rA 10-20 Rs
Weber Davis, ApJ, 148, 217, 1967
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Suns loss of angular momentum carried by the
solar wind II
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Yohkoh SXT The Changing Corona
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Changing corona and solar wind
45 30 15
0 -15
-30 -45
North Heliolatitude /
degree South
LASCO/Ulysses
McComas et al., 2000
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New solar wind data from Ulysses
Fast flow
V
n
McComas et al., 2000
Latitude - 65
September 3, 1999 - September 2, 2000
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Solar wind dropout
Subalfvénic flow
Helios 1 at 0.3 AU
Schwenn, 1980
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Coronal mass ejection
Observation by LASCO-C2 on SOHO.
Note the helical structure of the prominence
filaments!
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Speed profile of balloon-type CMEs
Wide range of initial acceleration 5-25 ms-2
Srivastava et al., 1999
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Speed profile of the slow solar wind
Parker, 1963
Speed profile as determined from plasma
blobs in the wind
Outflow starts at about 3 RS
Radial distance / RS
60
Sheeley et al., Ap.J., 484, 472, 1998
Consistent with Helios data
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Non-stationary slow solar wind

• Acceleration of slow wind above cusp (1)
• Coronal eruptions by magnetic reconnection
  inside the streamer (1)
• Interaction of three smaller streamers forming a
  dome (2)
• Plasmoids form by reconnection (3,4,5)

....small eruptions at the helmet streamer cusp
may incessantly accelerate small amounts of
plasma without significant changes of the
equilibrium configuration and might thus
contribute to the non-stationary slow solar
wind....
Wiegelmann et al., Solar Phys., 1999
36
Corona of the active sun
1998
EIT - LASCO C1/C2
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Solar wind models I
Assume heat flux, Qe - ???Te , is free of
divergence and thermal equilibrium T TpTe .
Heat conduction ? ?oT5/2 and ?o 8 108
erg/(cm s K) with T(?) 0 and T(0) 106K and
for spherical symmetry 4?r2?(T)dT/dr
const --gt T T0(R/r)2/7
Density ? npmpneme, quasi-neutrality
nnpne, thermal pressure p npkBTp nekBTe,
then with hydrostatic equilibrium and p(0) p0
dp/dr - GMmpn/r2
p p0 exp (7GMmp)/(5kBT0R) ( (R/r)5/7 -1)
Problem p(?) gt 0 , therefore corona must expand!
Chapman, 1957
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Proton and electron temperatures
slow wind ? fast wind
Electrons are cool!
fast wind ? slow wind
Protons are hot!
Marsch, 1991
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Solar wind models II
Density ? npmpneme, quasi-neutrality
nnpne, ideal-gas thermal pressure p npkBTp
nekBTe, thermal equilibrium T TpTe,
then with hydrodynamic equilibrium
mnpV dV/dr - dp/dr - GMmpn/r2 Mass
continuity equation
mnpV r2 J Assume an isothermal corona, with
sound speed c0(kBT0/mp)1/2, then one has to
integrate the DE
(V/c0)2 -1 dV/V 2 (1-rc/r) dr/r
With the critical radius, rc GMmp/(2kBT0)
(V?/2c0)2, and the escape speed, V? 618 km/s,
from the Suns surface.
Parker, 1958
40
Solar wind models III
Introduce the sonic Mach number as, Ms V/c0,
then the integral of the DE (C is an integration
constant) reads (Ms)2 - ln(Ms)2 4 ( ln(r/rc)
rc/r ) C For large distances, Ms gtgt 1 and V ?
(ln r)1/2, and n ? r-2/V, reflecting spherical
symmetry.
Only the wind solution IV, with C-3, goes
through the critical point rc and yields n -gt 0
and thus p -gt 0 for r -gt ?. This is Parkers
famous solution the solar wind.
Parker, 1958
V, solar breeze III accretion flow
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Fluid equations

• Mass flux FM ? V A ?
  npmpnimi
• Magnetic flux FB B A
• Total momentum equation
• Thermal pressure p npkBTp nekBTe
  nikBTi
• MHD wave pressure pw (?B)2/(8?)
• Kinetic wave acceleration aw (?pap
  ?iai)/?
• Stream/flux-tube cross section A(r)

V d/dr V - 1/? d/dr (p pw) - GMS/r2 aw
42
Temperature profiles in the corona and fast solar
wind
SP
SO
( Si 7)
Ti mi/mp Tp
( He 2)
Corona
Solar wind
Cranmer et al., Ap.J., 2000 Marsch, 1991
43
Energy equations
Parallel thermal energy
(Q??j S??j)/uj
w-p terms sources sinks
Perpendicularthermal energy
(Q?j S?j)/uj
Heating functions q?,? ? .... ? Wave
energy absorption/emission by wave-particle
interactions !
Conduction/collisional exchange of heat
radiative losses
44
Heating and acceleration of ions by cyclotron and
Landau resonance
aj acceleration 2 qj?? parallel
heating qj? perpendicular heating

Wave spectrum ? Wave dispersion ? Resonance
function ?
Marsch and Tu, JGR, 106, 227, 2001
45
Height profile of turbulence amplitude
Heliocentric distance / RS
SUMER Silicon VIII ??1440,1445 North polar
coronal hole
Doppler velocity V1/e / km s-1
At 1.33 RS
TSi ? 107 K ? ? 70 km s-1 ne ? 106 cm-3
Height above limb / arcsec
Wilhelm et al., Ap.J., 500, 1023, 1998
46
Rapid acceleration of the high-speed solar wind
Very hot protons
Up
T /K
V / km s-1
VA
Tp
Vp
L0.50 RS L0.25 RS
Te
Very fast acceleration
Radial distance / RS
Radial distance / RS
McKenzie et al., AA, 303, L45, 1995
Heating Q Q0 exp(- (r - RS)/L) Sonic
point r ? 2 RS
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Model of the fast solar wind
Low density, n ? 108 cm-3, consistent with
coronagraph measurements
N /cm-3

• hot protons, Tmax ? 5 M K
• cold electrons
• small wave temperature, Tw

Fast acceleration
T / K
V (VA) / km s-1
0 5 10
McKenzie et al., Geophys. Res. Lett., 24, 2877,
1997
Radial distance / RS
48
Anisotropic two-fluid model of the fast solar wind
Tp? 3 106 K

• Anisotropy weakly influences dynamics
• Anisotropy needed for perpendicular
  ion-cyclotron heating and thermodynamics

T /105 K

• Anisotropic heat deposition in 1-D two-fluid
  model
• Alfvén wave pressure gradient

Coronal base ?v ? 10-20 km s-1 ? ? 20-30 km
s-1
v / km s-1
Hu et al., JGR, 102, 14661, 1997
49
Two-dimensional two-fluid MHD model of the solar
corona
Heating function Qe,p Q0 fe,p(r,?)
exp(-0.1(r-Rs)/Rs) Q0 5 10-8 erg cm-3 s-1

• Time-dependent 2-D model MHD with separate Te
  and Tp equations
• Slow outflow at equator, fast over poles after 1
  day
• Heating functions Qe and Qp latitude-dependent

Poles Te lt Tp ? ?? 1 Equator Te
Tp ? ? 1
Suess et al., JGR, 104, 4697, 1999
Pole Co-latitude / Equator
50
Four-fluid model for turbulence driven heating of
coronal ions

• No wave absorption
• Turbulence spectra not self-consistent

• Four-fluid 1-D corona/wind model
• Quasi-linear heating and acceleration by
  dispersive ion-cyclotron waves
• Rigid power-law spectra with index -2 ? ? ? -1

Preferential heating of heavy ions by waves
Hu, Esser Habbal, JGR, 105, 5093, 2000
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The future Solar Orbiter
A high-resolution mission to the Sun and inner
heliosphere ESA 2011 - 2012
52
Solar Orbiters novel orbital design
Trajectory projection on ecliptic plane
- Closer to the Sun! - Out of the ecliptic!

• Venus gravity assist
• Solar electric propulsion